Why focus on spatial visualisations?

• Spatial case is a good example to work through because the aesthetics we have to express estimates are limited
• Maps take up most of the usual aesthetics by being a representation of space
  • position, size, shape, etc all have an implicit meaning in the mapping context
  • colour/fill is usually the only aesthetic we have left
  • can also get creative and do glyph maps (we will ignore this variation here)
• Once we have filled in a map, colour/fill is often the only aesthetic that has

Citizen Scientist Data

• There have been reports of a strange spatial pattern in the temperatures of Iowa
• We get some citizen scientists to measure data at their home and report back
• To maintain anonymity, we are only provided with the county of each scientist

990 citizen scientists participated

We could just plot the data…

• We often get spatial data in terms of longitude and latitude which we can plot directly

• This approach is easy but lacks the contextual information that gives our plots meaning.

Spatial features objects

• SF objects are differentiated from a tibble because of additional metata in the Coordinate reference system (CRS). Specifically:
  • Assumptions about the shape of the planet (geodetic datum)
  • Distortions we will/won’t accept when drawing the map (map projection)

Can you see the spatial trend?

Estimate the county mean

• Visualising an estimate, such as a mean, can make trends easier to see
  • Should use the sampling distribution, but often we do not bother…

# Calculate County Mean
toy_temp |> 
  group_by(county_name) |>
  summarise(temp_mean = mean(recorded_temp),
            temp_se = sd(recorded_temp)/sqrt(n()),
            n = n()) 

Can you see the trend now?

Common Map Visualisations

Spot the difference

Exercise 1

Make the high and low variance choropleth maps yourself, and see why they come out looking identical

Solution 1: add an axis for uncertainty

• Pro
  • Included uncertainty and increased transparency
• Cons
  • High uncertainty signal still very visible
  • 2D palette is harder to read
    • Colour is not a simple 3D space
    • Using saturation hurts accessibility

Solution 2: blend the colours together

• Pros
  • Included uncertainty and increased transparency
  • Removed false signals
• Cons
  • Still have 2D Colour palette
  • Standard error at which to blend colours is made up
    • Impossible to align with hypothesis testing

Solution 3: simulate a sample

• Pros
  • Included uncertainty
  • High uncertainty interferes with reading of plot (?)
  • 1D colour palette

Popular R packages

• ggdibbler
  • Data: distribution from distributional
  • Maps: pixel map, other non-spatial maps
• Vizumap
  • Data: Depends on the plot. Can take a distribution as a q function (pixel), or an estimate and standard error as two variables (bivar/VSUP and glyph)
  • Maps: Biar/VSUP, pixel, glyph
• biscale
  • Data: Estimate and standard error as two variables
  • Maps: Biar/VSUP map

Estimate the county distribution

• Visualising an estimate, such as a mean, can make trends easier to see
  • Should use the sampling distribution, but often we do not bother…

Using ggdibbler to plot a Distribution

toy_temp_dist |> 
  ggplot() + 
  geom_sf_sample(aes(geometry = county_geometry,
                     fill=temp_dist_low))

toy_temp_dist |> 
  ggplot() + 
  geom_sf_sample(aes(geometry = county_geometry,
                     fill=temp_dist_high))

Can utilise ggplot2 flexibility

Can utilise ggplot2 flexibility

Remember, the plot is random

Exercise 2

Here is the code that was used to make the cartogram from earlier in the session. Can you make a ggdibbler verion of this plot?

# Transform to a the crs needed to do the cartogram transformation
toy_merc <- st_transform(toy_temp_mean, 3857)
# cartogram transformation
toy_cartogram <- cartogram_cont(toy_merc, weight = "n", itermax = 5)
# Transform back to original crs 
toy_cartogram <- st_transform(toy_cartogram, st_crs(toy_temp_mean))

# Plot cartogram using ggplot2
ggplot(toy_cartogram) +
  geom_sf(aes(fill = temp_mean), linewidth = 0, alpha = 0.9) +
  theme_minimal() +
  scale_fill_distiller(palette = "YlOrRd", direction= 1) +
  xlab("Longitude") +
  ylab("Latitude") +
  labs(fill = "Temperature") +
  theme(aspect.ratio=0.7)

Solution

# only change to data is distribution
toy_cartogram |>
  mutate(temp_dist = distributional::dist_normal(temp_mean, temp_se^2)) |>
  ggplot() +
  geom_sf_sample(aes(geometry=county_geometry, 
                     fill=temp_dist), linewidth=0) +
   geom_sf(aes(geometry=county_geometry), fill=NA, colour="white") +
  theme_minimal() +
  scale_fill_distiller(palette = "YlOrRd", direction= 1) +
  xlab("Longitude") +
  ylab("Latitude") +
  labs(fill = "Temperature") +
  theme(aspect.ratio=0.7)

Where to learn more

• Kay, M. ggdist: Visualizations of distributions and uncertainty
• Hofmann, Follett, Majumder, Cook 2012 Graphical Tests for Power Comparison of Competing Designs
• nullabor package
• Spiegelhalter, D. (2017), Risk and uncertainty communication